Solve frac{x^{20}y^9z^2}{x^5y^9z}

$$\frac { x ^ { 20 } y ^ { 9 } z ^ { 2 } } { x ^ { 5 } y ^ { 9 } z }$$

Differentiate w.r.t. x

$$15zx^{14}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{z^{2}y^{9}}{zy^{9}}x^{20-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(zx^{15})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$15zx^{15-1}$$

Do the arithmetic.

$$15zx^{14}$$

Evaluate

$$zx^{15}$$

Solution Steps

Cancel out zx^{5}y^{9} in both numerator and denominator.

$$zx^{15}$$